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Partially well-ordered closed sets of permutations M. D. Atkinson
 

Summary: Partially well-ordered closed sets of permutations
M. D. Atkinson
Department of Computer Science
University of Otago, New Zealand
M. M. Murphy
School of Mathematics and Statistics
University of St Andrews, UK
N. Ruskuc
School of Mathematics and Statistics
University of St Andrews, UK
Abstract
It is known that the \pattern containment" order on permutations
is not a partial well-order. Nevertheless, many naturally de ned sub-
sets of permutations are partially well-ordered, in which case they have
a strong nite basis property. Several classes are proved to be partially
well-ordered under pattern containment. Conversely, a number of new
antichains are exhibited that give some insight as to where the boundary
between partially well-ordered and not partially well-ordered classes lies.
Keywords Permutation, pattern containment, involvement, nite basis, partial
well-order

  

Source: Atkinson, Mike - Department of Computer Science, University of Otago
St Andrews, University of - School of Mathematics and Statistics, Centre for Interdisciplinary Research in Computational Algebra

 

Collections: Computer Technologies and Information Sciences; Mathematics